Application of KWW Function and Cole–Cole Plot on Stress Relaxation Process of Magnolia Obovata Wood

Abstract

The stress relaxation mechanism of hardwood (Magnolia obovata Thunb.) was analyzed using the Kohlrausch–Williams–Watts (KWW) function and a Cole–Cole plot to elucidate the effects of moisture content and static displacement. The relationship between relaxation modulus of elasticity and moisture content was examined in a stress relaxation test, which was performed for one week at a stress ratio of 35%. Two linear regions appeared in the double logarithmic relaxation modulus plot against logarithmic time. The stretching parameters and specific relaxation times were obtained by fitting the KWW function to the relaxation data. The specific relaxation time was the shortest at a moisture content of 6–8%. The effect of static displacement on stress relaxation was examined using dynamic mechanical analysis, which was performed for 1 h at stress ratios of 11% and 33%. At a stress ratio of 11%, the relaxation modulus ratio to logarithmic time changed after 0.1 h. Both the former and latter relaxation processes can be fitted to Cole–Cole circles. At a stress ratio of approximately 33%, the change in storage modulus ratio over logarithmic time changed in the later period, whereas it monotonously increased at a stress ratio of 11%. Only the former relaxation data could be fitted into the Cole–Cole circle; however, the latter relaxation process could not be fitted. A stress ratio of 35%, which was applied in the stress relaxation test, may be out of linear viscoelasticity.